I've found excellent jobs via the "Career" section of a company's website, via recruiters off LinkedIn, and via a combination of job post online combined with finding the recruiters information at the company and contacting them directly to apply.
My approach was very successful. Less than two months after graduating with my BS in Economics I landed a excellent paid internship ($40,000/yr) in Credit Risk Analysis at a large regional bank. Three months later I was promoted to Credit Risk Analyst and given a raise to $51,000/yr + all the nice bank benefits.
So yes, it can be done. My approach included a healthy dose of determination, precision targeting of applications to recruiters and hiring managers, personalization of my application package to the job post, and being a well-prepared candidate who presents well. Apply for jobs you're actually interested, address what they're looking for in your cover-letter and resume, as much as possible get your application materials to hiring managers or recruiters directly, always dress and behave with class (wear a tailored suit to your interviews, shower, shave, and put your best foot forward), and never give up.
The problem is that most people adopt some of the worst job-hunting techniques imaginable. They write one resume and one cover-letter and then just send the combination out to every job they can think of. They bombard "Career" websites with derivative forgettable applications that may not have any apparent relation to the position advertised. Then should they get an interview, they may or may not show up, and may or may not put the time into presenting themselves in the best possible light. In short: many job seekers these days are super lazy (to put it very bluntly). They act entitled to a good job with a minimum of effort.
When I was interviewing I couldn't believe the other candidates I saw out there. They'd show up in ill-fitting ratty jeans, a wrinkled tie, with a three-week overgrowth of facial hair and grumpy demeanor. Just seeing them in the waiting area I thought there's no way I'd ever hire any of those people no matter what they had on their resume.
And sometimes interviewees wouldn't even show for their scheduled interview. When I worked at the bank, one candidate for a very high-paying position didn't bother to call and didn't bother to show the first time she scheduled an interview. Then she had the gall to call later, offer no reason for her no-show/no-call previously and reschedule another interview...which she also didn't show up for. Unbelievable.
In other words, if you are truly a "professional" and convey it in every way in your job hunt, you will find a "good job" one way or another--traditional hiring system or not. I hope this helps!